Neutrino Mass Spectrum from M-Theory Compactification on G₂-Holonomy Manifolds: Seesaw Mechanism with Flux-Derived Instanton Action Gap and E₈ CP Protection

The neutrino mass spectrum is derived from first principles within the Quantum Geometric Unification (QGU) framework based on M-theory compactification on the Joyce orbifold T⁷/ (Z₃ ⋉ I*) with G₂ holonomy. Right-handed neutrino Majorana masses are generated by M2-brane instantons wrapping associative three-cycles at the three conical singularities, with the intermediate scale fixed by the SUGRA hierarchy relation as Mₑ, ₂ = √α₄₌ × Mcomp = 1. 71 × 10¹⁵ GeV. The instanton action gap δS = 1. 746 is derived from the N=1 SUGRA scalar potential with flux superpotential W₀ = -nf dim (G₂) / (2π) K₀^-3/7 = -0. 486, determined by the G₂ identity ∫*φ∧φ = 7 Vol (X₇) and flux quantisation with N = 3 quanta. The complete mass spectrum m₁ = 1. 56, m₂ = 8. 87, m₃ = 50. 6 meV reproduces Δm²₂₁ and Δm²₃₂ to 1. 3% and 1. 2% respectively. PMNS angles emerge from Z₃ symmetry: sin²θ₁₂ = 0. 303 (0. 3σ) and sin²θ₂₃ = 0. 542 (0. 2σ). Compatibility with baryogenesis via leptogenesis is demonstrated (ηBᵐax/ηBᵒbs ≈ 9), with CP violation protected at leading order by the even rank of E₈ (spectral flow = 8 ≡ 0 mod 2). Five testable predictions include Σm_ν = 61 meV (within DESI sensitivity). All mass ratios employ zero adjustable parameters beyond three geometric constants established independently in eight companion publications.